Cremona's table of elliptic curves

909 = 3² · 101

Field	Data	Notes
Atkin-Lehner	3- 101-	Signs for the Atkin-Lehner involutions
Class	909c	Isogeny class
Conductor	909	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	73629 = 36 · 101	Discriminant
Eigenvalues	0 3-  1 -2  2  1 -3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-12,9]	[a1,a2,a3,a4,a6]
Generators	[-1:4:1]	Generators of the group modulo torsion
j	262144/101	j-invariant
L	2.1205886994754	L(r)(E,1)/r!
Ω	3.1448957011688	Real period
R	0.33714769915697	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	14544x1 58176j1 101a1 22725j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 909c1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
0	-	1	-2	2	1	-3	-5	-1	4	-9	-2	-8	-8	-7	2	14	4	2	-13	8	-9	4	-14	2

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Quadratic twists for elliptic curve 909c1

-4	8	-3	5	-7	-11	101
14544x1	58176j1	101a1	22725j1	44541c1	109989e1	91809c1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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